Lab Report on Chemical Kinetics (Initial Rates Method & Activation Energy from the Temperature Dependence of the Reaction Rate)

The lab report below was submitted as part of the coursework for CM1131 Basic Physical Chemistry. Please do not plagiarise from it as plagiarism might land you into trouble with your university. Do note that my report is well-circulated online and many of my juniors have received soft copies of it. Hence, please exercise prudence while referring to it and, if necessary, cite this webpage.

1. Aim: To determine the reaction orders and rate constant of a chemical reaction, using the method of initial reaction rates as well as to determine the activation energy from the temperature dependence of the reaction rate based on Arrhenius’ theory.

2. Results & Calculations:

2.1 Determination of Reaction Orders and Rate Constant

Molarity of KI:                   0.2000M

Molarity of S₂O₈^2- :           0.1000M

Molarity of S₂O₃^2-:            0.003300M

Solution	Vol. S2O82- (mL)	Vol. I- (mL)	Vol. H2O (mL)	Vol. Starch (mL)	Vol. S2O32- (mL)	Time (s)	Time (s)	Average Time (s)
1	10	10	0	1	5	20	20	20
2	10	8	2	1	5	24	24	24
3	10	6	4	1	5	35	36	35.5
4	10	5	5	1	5	46	45	45.5
5	10	3	7	1	5	77	82	79.5
6	10	10	0	1	5	20	20	20
7	8	10	2	1	5	25	25	25
8	6	10	4	1	5	35	36	35.5
9	5	10	5	1	5	41	39	40
10	3	10	7	1	5	86	83	84.5

Q1. Total volume of solution in the conical flask for each reaction is 26mL = 26cm^-3

In Solution 1 to 5:             [S₂O₈^2-]                 = (0.01 × 0.1) ÷ 0.026                       = 0.03846 moldm^-3

In Solution 1:                      [I^-]                          = (0.01 × 0.2) ÷ 0.026                       = 0.07692 moldm^-3

In Solution 2:                      [I^-]                          = (0.008 × 0.2) ÷ 0.026                    = 0.06154 moldm^-3

In Solution 3:                      [I^-]                          = (0.006 × 0.2) ÷ 0.026                    = 0.04615 moldm^-3

In Solution 4:                      [I^-]                          = (0.005 × 0.2) ÷ 0.026                    = 0.03846 moldm^-3

In Solution 5:                      [I^-]                          = (0.003 × 0.2) ÷ 0.026                    = 0.02308 moldm^-3

In Solution 6 to 10:           [I^-]                          = (0.01 × 0.2) ÷ 0.026                       = 0.07692 moldm^-3

In Solution 6:                      [S₂O₈^2-]                 = (0.01 × 0.1) ÷ 0.026                       = 0.03846 moldm^-3

In Solution 7:                      [S₂O₈^2-]                 = (0.008 × 0.1) ÷ 0.026                    = 0.03077 moldm^-3

In Solution 8:                      [S₂O₈^2-]                 = (0.006 × 0.1) ÷ 0.026                    = 0.02308 moldm^-3

In Solution 9:                      [S₂O₈^2-]                 = (0.005 × 0.1) ÷ 0.026                    = 0.01923 moldm^-3

In Solution 10:                   [S₂O₈^2-]                 = (0.003 × 0.1) ÷ 0.026                    = 0.01154 moldm^-3

Solution	[S2O82-] (moldm-3)	[I-] (moldm-3)	Time (s)	Time (s)	Average Time (s)	ln[S2O82-]	ln[I-]
1	0.03846	0.07692	20	20	20	-3.258	-2.565
2	0.03846	0.06154	24	24	24	-3.258	-2.788
3	0.03846	0.04615	35	36	35.5	-3.258	-3.076
4	0.03846	0.03846	46	45	45.5	-3.258	-3.258
5	0.03846	0.02308	77	82	79.5	-3.258	-2.565
6	0.03846	0.07692	20	20	20	-3.258	-2.565
7	0.03077	0.07692	25	25	25	-3.481	-2.565
8	0.02308	0.07692	35	36	35.5	-3.769	-2.565
9	0.01923	0.07692	41	39	40	-3.951	-2.565
10	0.01154	0.07692	86	83	84.5	-4.462	-2.565

Q2. Reaction between I₂ and S₂O₃^2-:                        I₂+2S₂O₃^2-            2I^-+  S₄O₆^2-

No. of moles of S₂O₃^2- reacted   =(5 x 10^-3) × 0.003300      = 1.650 × 10^-5mol

Since I₂ ≡ 2S₂O₃^2-, no. of moles of I₂ reacted = ½(1.650 × 10^-5) = 8.250× 10^-6mol

Therefore, no. of moles of I₂ reacted/L= 8.250× 10^-6 ÷ 0.026 = 3.173 × 10^-4 molL^-1

Rate of reaction of:

Solution 1            = 3.173 × 10^-4 molL^-1 ÷ 20s                             = 1.587 × 10^-5 molL^-1s^-1

Solution 2            = 3.173 × 10^-4 molL^-1 ÷ 24s                             = 1.322 × 10^-5 molL^-1s^-1

Solution 3            = 3.173 × 10^-4 molL^-1 ÷ 35.5s                         = 8.938 × 10^-6 molL^-1s^-1

Solution 4            = 3.173 × 10^-4 molL^-1 ÷ 45.5s                         = 6.973 × 10^-6 molL^-1s^-1

Solution 5            = 3.173 × 10^-4 molL^-1 ÷ 79.5s                         = 3.991 × 10^-6 molL^-1s^-1

Solution 6            = 3.173 × 10^-4 molL^-1 ÷ 20s                             = 1.587 × 10^-5 molL^-1s^-1

Solution 7            = 3.173 × 10^-4 molL^-1 ÷ 25s                             = 1.269 × 10^-5 molL^-1s^-1

Solution 8            = 3.173 × 10^-4 molL^-1 ÷ 35.5s                         = 8.938 × 10^-6 molL^-1s^-1

Solution 9            = 3.173 × 10^-4 molL^-1 ÷ 40s                             = 7.932 × 10^-6 molL^-1s^-1

Solution 10          = 3.173 × 10^-4 molL^-1 ÷ 84.5s                         = 3.755 × 10^-6 molL^-1s^-1

Q3.

Solution	[I-] molL-1	ln[I-]	[S2O82-] molL-1	ln[S2O82-]	Rate (R) molL-1s-1	ln R
1	0.07692	-2.565	0.03846	-3.258	1.587 × 10-5	-11.05
2	0.06154	-2.788	0.03846	-3.258	1.322 × 10-5	-11.23
3	0.04615	-3.076	0.03846	-3.258	8.938 × 10-6	-11.63
4	0.03846	-3.258	0.03846	-3.258	6.973 × 10-6	-11.87
5	0.02308	-3.769	0.03846	-3.258	3.991 × 10-6	-12.43
6	0.07692	-2.565	0.03846	-3.258	1.587 × 10-5	-11.05
7	0.07692	-2.565	0.03077	-3.481	1.269 × 10-5	-11.27
8	0.07692	-2.565	0.02308	-3.769	8.938 × 10-6	-11.63
9	0.07692	-2.565	0.01923	-3.951	7.932 × 10-6	-11.74
10	0.07692	-2.565	0.01154	-4.462	3.755 × 10-6	-12.49

Table 2.1.2: Values for the logs of [I^-], [S₂O₈^2-] and the rate R.

Q4. Gradient of best-fit-line (n) is 1.1781.

 

From the graph, the equation of best fit line is y=1.1781x-8.0004 where y = ln R and x = ln[I^-]. The gradient of the graph is 1.1781 and thus, reaction order with respect to [I^-], n=1.1781≈1 (to nearest integer).

Q5. Gradient of best-fit-line (m) is 1.1861.

 

From the graph, the equation of best fit line is y=1.1861x-7.1477 where y = ln R and x = ln[S₂O₈^2-]. The gradient of the graph is 1.1861 and thus, reaction order with respect to ln[S₂O₈^2-],n=1.1861≈1 (to nearest integer).

Q6.

Since n = 1.216 ≈ 1 and m = 1.247 ≈ 1 (nearest integer),

Since n = 1.216 ≈ 1 and m = 1.247 ≈ 1 (nearest integer)

Solution	[I-] molL-1	[S2O82-] molL-1	Rate (R) molL-1s-1	k
1	0.07692	0.03846	1.587 × 10-5	0.005364
2	0.06154	0.03846	1.322 × 10-5	0.005586
3	0.04615	0.03846	8.938 × 10-6	0.005036
4	0.03846	0.03846	6.973 × 10-6	0.004714
5	0.02308	0.03846	3.991 × 10-6	0.004496
6	0.07692	0.03846	1.587 × 10-5	0.005364
7	0.07692	0.03077	1.269 × 10-5	0.005362
8	0.07692	0.02308	8.938 × 10-6	0.005035
9	0.07692	0.01923	7.932 × 10-6	0.005362
10	0.07692	0.01154	3.755 × 10-6	0.004230

Table 2.1.3: Determined values for m, n and k.

Q7. Average value of k  = = 5.055 × 10^-3 mol^-1Ls^-1

Standard deviation,                = 4.437 × 10^-4mol^-1Ls^-1

2.2 Temperature Effect on a Chemical Reaction

	Temp (0C)	Temp (K)	1/T (K-1)	Time (s)	Time (s)	Average Time (s)	ln(t)
1	59.0	332.15	0.003011	11	10	11	2.398
2	44.0	317.15	0.003153	20	18	19	2.944
3	31.0	304.15	0.003288	76	75	76	4.331
4	20.5	293.65	0.003405	338	-	338	5.823
5	8.0	281.15	0.003557	1242	-	1242	7.124

Table 2.2.1: Average time taken for the mixture of solution to turn blue at different temperatures. Temperature was kept constant for each experiment.

Graph 2.2.1: ln t against 1/T with temperature kept constant for each experiment

Since E_A/R = 9142.5K,

Therefore E_A         = 9142.5K × 8.314 JK^-1mol^-1

                                = 76010 Jmol^-1

                                = 76.01 KJmol^-1
Gradient of graph (i.e. E_A/R) is 9142.5

3. Discussion:

3.1 Determination of Reaction Orders and Rate Constant

The experiments are conducted based on the rate equation, R = k [I-]ⁿ[S₂O₈^2-]^m, where k is the rate constant while n and m are the reaction orders of I^- and S₂O₈^2- respectively. As reaction orders, n and m is defined as the power to which the concentration of that reactant is raised to in the experimentally determined rate equation.nand mcannot be found theoretically and are experimentally determined to be 1. This means that the reaction is first order with respect to [I^-] and first order with respect to [S₂O₈^2-]. The overall rate order is 2.This reaction is said to be bimolecular since two reactant species are involved in the rate determining step.

It was observed that the rate of reaction increases with increasing concentration. The Collision Theory explains the phenomenon by stating that for a chemical reaction to occur, reactant molecules must collide together in the proper orientation and the colliding molecules must possess a minimum energy known as the activation energy, E_A, before products are formed. An increase in the concentration of reactants leads to an increase in the number of reactant molecules having energy ≥ E_A, hence increasing the collision frequency. The increase in the effective collision frequency leads to an increase in the reaction rate.

When performing a chemical kinetics experiment, the procedures have to be conducted at a constant temperature. According to the Arrhenius equation,

k=Ae^-Ea/RT, a slight increase in temperature increases reaction rate significantly as the equation is exponential in nature. This is affirmed by the Maxwell-Boltzmann distribution curve (diagram on the right) as a slight increase in temperature increases the number of colliding particles with E_a and consequently, reaction rates, significantly.

Hence, because slight deviations in temperature may affect reaction rates significantly, the temperature at which the experiment was carried out must be kept constant.

To prevent errors from occurring, all glassware used in this experiment must be kept clean and dry to prevent contamination by the previous batch of experimental products. The overall volume of the solution was also kept constant at 26mL by adding deionized water, to standardize the conditions of the reaction environment, thus increasing accuracy.

Swirling of the conical flask contents for the same length of time must be done consistently so that results obtained will be fair. Instead of swirling with one’s hands, the conical flasks can be placed on an electronic swirl to ensure consistent swirling when conducting the experiment.

Also, there is inaccuracy as the stopwatch was stopped only when an arbitrary colour intensity was observed. There should be a consensus between lab partners as to when the stopwatch should be stopped.

3.2 Temperature Effect on a Chemical Reaction

The results of this set of experiment show that the rate of reaction increases as temperature increases. Using the Arrhenius equation, k=Ae^-Ea/RT, the activation energy, E_A, can be determined by keeping the concentration of all the reactants constant while varying the temperature for each experiment.

When performing a chemical kinetics experiment, the procedures have to be conducted at a constant temperature. According to the Arrhenius equation,

k=Ae^-Ea/RT, a slight deviation in temperature changes reaction rate significantly. This is affirmed by the Maxwell-Boltzmann distribution curve (diagram on the right) as a slight increase in temperature increases the number of colliding particles with E_aand consequently, reaction rates, significantly.

Hence, since slight deviations in temperature may affect reaction   rates significantly, the temperature at which the experiment was carried out must be kept constant.

This is especially important for experiments being conducted at 10^oC and 20^oC, the conical flasks were placed in an ice bath to maintain the reaction temperature. There were several fluctuations above and below the desired temperatures. Moreover, the time taken for the blue solution to turn colourless is relatively longer for these 2 lower temperatures which creates a greater room for error. Keeping temperatures constant can be done by conducting the experiments in a thermostatic water bath.

Reactants were poured imprecisely into the conical flask. There may be leftover reactants in the test tubes and some reactants may stain the sides of the conical flask during the addition. This reduces the concentration of the reactants in the conical flask. Pipetting the reactants into the conical flask would ensure that the reactants are added in the requisite quantities and that the eventual results are accurate.

Swirling of the conical flask contents for the same length of time must be done consistently so that results obtained will be fair. Instead of swirling with one’s hands, the conical flasks can be placed on an electronic swirl to ensure consistent swirling when conducting the experiment.

Also, there is inaccuracy as the stopwatch was stopped only when an arbitrary colour intensity was observed. There should be a consensus between lab partners as to when the stopwatch should be stopped.

The reaction is autocatalysed as the product of the reaction acts as a catalyst for the reaction. An autocatalysed reaction is slow at first and then becomes more rapidly as the catalyst is produced in the reaction. For the reaction, Mn²⁺ is the autocatalyst. This accounts for why vigorous effervescence of CO₂ is not observed immediately when the reactants were added but only observed after a little while when Mn²⁺ is produced.

2MnO₄^2- + 5C₂O₄^2- + 16H⁺ -> 2Mn²⁺+10 CO₂ + 8H₂O

4. Conclusion:

The rate equation of the chemical reaction between I^- and S₂O₈^2- to produce I₂ and SO₄^2- has been found to be:

 Rate = k[I-][S₂O₈^2-],        where rate constant k =5.055 × 10^-3 mol^-1Ls^-1

The reaction is first order with respect to [I^-] and the reaction is first order with respect to [S₂O₈^2-]. The overall order of reaction is 2. This reaction is said to be bimolecular since two reactant species are involved in the rate determining step.

Using the Arrhenius equation, k=Ae^-Ea/RT, the activation energy, E_A, of the oxidation reaction of oxalic acid by permanganate was determined to be 76.01KJmol^-1. This means that the minimum amount of energy that reactant particles must possess in order to react successfully is experimentally determined to be 76.01KJmol^-1.

5. References:

1)http://www.shodor.org/unchem/advanced/kin/arrhenius.html

2)http://www.webchem.net/notes/how_far/kinetics/maxwell_boltzmann.htm

3)http://jchemed.chem.wisc.edu/JCESoft/CCA/CCA3/MAIN/AUTOCAT/PAGE1.HTM